Once logged into office.com, click on the Apps icon on the left of the screen:

Then click on the icon representing the app you wish to use, like Word:

Under ‘Create’, click on ‘Blank document’:

Click on the little right arrow next to ‘Open’, then click on 'Open files from this device

Browse to the location where your file exists, highlight it, and click ‘Open’.
You may see a message that says your file is being uploaded to ‘My Files’ in OneDrive… if you don’t see it, check your browser for pop-up blockers“. This message may disappear quite quickly!

If your document does not open in a new tab, as expected, look at the far right of the URL in your browser. You will see this little notice saying “Pop-up blocked”. Click on it, then click the radio button for ‘Always allow..”, then click 'Done’. You will only need to do this once.

Your document should open in a new tab.